He thus laid the way open for the view, which we adopt, that every assertion of a particular causal connexion involves the assertion of a causal law, and that every general proposition of the form ‘C causes E’ is equivalent to a proposition of the form ‘whenever C, then E’, where the symbol ‘whenever’ must be taken to refer, not to a finite number of actual instances of C, but to the infinite number of possible instances. He himself defines a cause as ‘an object, followed by another, and where all the objects similar to the first are followed by objects similar to the second’, or, alternatively, as ‘an object followed by another, and whose appearance always conveys the thought to that other’;5 but neither of these definitions is acceptable as it stands. For, even if it is true that we should not, according to our standards of rationality, have good reason to believe that an event C was the cause of an event E unless we had observed a constant conjunction of events like C with events like E, still there is no self-contradiction involved in asserting the proposition ‘C is the cause of E’ and at the same time denying that any events like C or like E ever have been observed; and this would be self-contradictory if the first of the definitions quoted was correct. Nor is it inconceivable, as the second definition implies, that there should be causal laws which have never yet been thought of. But although we are obliged, for these reasons, to reject Hume’s actual definitions of a cause, our view of the nature of causation remains substantially the same as his.
Let's take a more precise look at this part:
For, even if it is true that we should not, according to our standards of rationality, have good reason to believe that an event C was the cause of an event E unless we had observed a constant conjunction of events like C with events like E, still there is no self-contradiction involved in asserting the proposition ‘C is the cause of E’ and at the same time denying that any events like C or like E ever have been observed; and this would be self-contradictory if the first of the definitions quoted was correct.
Why if we accept Hume's first definition would it be self contradiction to say 'C is the cause of E' and 'C and E have never been observed' at the same time?
Can you give me logical formula to support your answer?
